The present invention relates to a new and distinct raspberry cultivar designated ‘DrisRaspTwo’ and botanically known as Rubus ideaus L. This new raspberry variety was discovered in Santa Cruz, Calif. in May 2004 and originated from a cross between the female parent raspberry plant ‘Driscoll Cardinal’ (U.S. Plant Pat. No. 14,903) and the proprietary male parent raspberry plant ‘W776.1’ (unpatented). The original seedling of the new cultivar was asexually propagated by stolons or tissue culture, at a nursery in Santa Cruz, Calif. ‘DrisRaspTwo’ was subsequently asexually propagated and underwent further testing at a nursery in Santa Cruz, Calif. for five years. The present invention has been found to be stable and reproduce true to type through successive asexual propagations.